一类非线性方程Mann和Ishikawa迭代程序的稳定性

Stability of Mann and Ishikawa Iterative Processes for a Class of Nonlinear Equations

设X是实Banach空间,H:X→X是Lipschitz算子,T:X→X是一致连续的且值域有界,H+T是强增生的,则Mann和Ishikawa迭代程序几乎稳定地强收敛到方程Hx+Tx=f的唯一解.

Suppose that X is a real Banach space, H:X→X is Lipschitz operator, T:X→X is uniformly continuous with bounded range, H+T is strongly accretive. Then Mann and Ishikawa iterative processes converge strongly, almost stably, to the unique solution of the equation Hx+Tx=f.